Heterodyne Detector for Measuring the Characteristic of Elliptically Polarized Microwaves

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Heterodyne detector for measuring the characteristic of elliptically polarized microwaves

Leipold, Frank; Nielsen, Stefan Kragh; Michelsen, Susanne

Published in: Review of Scientific Instruments

Link to article, DOI: 10.1063/1.2937651

Publication date: 2008

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Citation (APA): Leipold, F., Nielsen, S. K., & Michelsen, S. (2008). Heterodyne detector for measuring the characteristic of elliptically polarized microwaves. Review of Scientific Instruments, 79(6), 065103. https://doi.org/10.1063/1.2937651

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REVIEW OF SCIENTIFIC INSTRUMENTS 79, 065103 ͑2008͒

Heterodyne detector for measuring the characteristic of elliptically polarized microwaves Frank Leipold, Stefan Nielsen, and Susanne Michelsen Association EURATOM, Risø National Laboratory, Technical University of Denmark, OPL-128, Frederiksborgvej 399, 4000 Roskilde, Denmark ͑Received 28 January 2008; accepted 6 May 2008; published online 4 June 2008͒ In the present paper, a device is introduced, which is capable of determining the three characteristic parameters of elliptically polarized light ͑ellipticity, angle of ellipticity, and direction of rotation͒ for microwave radiation at a frequency of 110 GHz. The device consists of two perpendicular orientated pickup waveguides. A heterodyne technique mixes the microwave frequency down to frequencies on the order of 200 MHz. An oscilloscope is used to determine the relative amplitudes of the electrical ﬁelds and the phase shift in between, from which the three characteristic parameters can be calculated. Results from measured and calculated wave characteristics of an elliptically polarized 110 GHz microwave beam for plasma heating launched into the TEXTOR-tokamak experiment are presented. Measurement and calculation are in good agreement. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2937651͔

INTRODUCTION characteristics obtained by polarizer plates in the transmis- Elliptically polarized microwaves in the range above sion line can be calculated from the orientation of the polar- ͑ ͒ 100 GHz play an important role for plasma heating, current izer plates when their characteristics are known . However, drive, and scattering of radiation in tokamak plasma it is desirable to verify the calculated results by measure- experiments.1,2 High power microwave sources ͑gyrotrons͒ ments. are used for these applications. A gyrotron generates linearly Elliptically polarized light is obtained, when two perpen- polarized waves. In order to transform a linearly polarized dicularly orientated linearly polarized waves with a phase wave into an elliptically polarized wave, polarizer plates are shift are superimposed. The propagation directions of both employed.3,4 A polarizer plate is a mirror with parallel waves is the z direction and Ex and Ey are the electrical field grooves on the surface. In a simplified picture, an electrical components in the x and y directions, respectively. Figure 1 ͑ ͒ field component which is oriented parallel to the grooves is shows an example of two waves Ex and Ey with a phase / reflected on top of the grooves. The electrical field compo- shift of 50°. The ratio of the amplitudes Ey Ex is 0.7. Figure nent, which is oriented perpendicular to the grooves is re- 2 shows the projection of the electrical field in the x-y plane. flected at the bottom of the grooves. This causes a phase shift The strength of the electrical field is represented by the dis- with respect to the electrical field component reflected on top tance between the origin and the boundary of the ellipse. The of the grooves. A detailed description of the diffraction of electrical field vector rotates, as described in the picture. electromagnetic waves with perfectly electrical conducting The characteristic of elliptically polarized light can be rectangular grooved grating is described in Ref. 5. The phase described by three parameters: ellipticity ͑␧͒, angle of ellip- 8–10 shift depends on the design of the polarizer plate. The groove ticity ͑⌰͒, and direction of rotation ͑␳͒. ␧ is the ratio of depths and width are dependent on the used frequency and the minor axis to the major axis of the ellipse describing the the desired phase shift. The superposition of both electrical electrical field in the x-y plane. It varies between 0 ͑linearly field components provides, in general, elliptically polarized polarized light͒ and 1 ͑circularly polarized light͒. ⌰ is the waves. angle between the major axis of the ellipse and the x axis in Characterization of elliptically polarized microwaves in turning direction toward the y axis ͑mathematically positive the frequency range of 110 GHz is important, e.g., for the direction͒. It varies between 0° and 180°. ␳ can either be diagnostic technique of collective Thomson scattering.6,7 left-hand polarized or right-hand polarized. The electrical This technique uses a probing microwave beam launched field vector of a right-hand polarized wave propagating in the into the plasma and detects scattered light leaving the positive z direction in a right handed coordinate system ro- plasma. Probing beam and scattered signal are generally el- tates in the mathematically negative direction when projected liptically polarized. In the case of the probing beam, the re- into the x-y plane. The transformation from the parameters, quired elliptically polarized light is obtained by transforming Ex, Ey, and phase shift between Ex and Ey to the character- linearly polarized waves from a gyrotron by means of a set istic parameters ⌰, ␧, and ␳ is described in detail in Ref. 8. of two polarizer plates. The elliptically polarized scattered In the example above ͑Figs. 1 and 2͒, the angle of ellipticity signal leaving the plasma is transformed by means of polar- ⌰ is 30.2°, the ellipticity ␧ is 0.42, and the rotation ␳ is izer plates into linearly polarized light which can be accepted right-hand polarized. by the receiver. Theoretically, the elliptically polarized wave ␧ and ⌰ of elliptically polarized waves can be obtained

Downloaded 13 Aug 2009 to 192.38.67.112. Redistribution subject to AIP license or copyright; see http://rsi.aip.org/rsi/copyright.jsp 065103-2 Leipold, Nielsen, and Michelsen Rev. Sci. Instrum. 79, 065103 ͑2008͒

FIG. 3. Schematic of the detector for elliptically polarized light.

second step, the y component of the electrical field is phase shifted by 90° degrees, and again, sum and difference signals are recorded. These four values allow the characterization of the elliptically polarized waves. The present article reports about a two-channel heterodyne detection system which is built in order to fully char- ͑ ͒ FIG. 1. The relative electrical field strength in the directions of x Ex and y acterize elliptically polarized waves instantaneously without ͑E ͒ E E y . In this example, y leads x by 50°. the use of movable mechanical parts. Principles of heterodyne techniques can be found in Refs. 13 and 14. by detecting the light intensity in various orientations of a detector diode in the x-y plane. This technique does not re- quire a complex system. However, since the phase difference DEVICE SETUP of the measured electrical field in various directions cannot The intensity of microwave radiation can easily be mea- be detected, the rotation of the elliptically polarized wave sured by detector diodes or Schottky diodes, but this tech- cannot be obtained in this approach. Furthermore, several nique does not provide information about the phase between measurements in various orientations of the detector are re- the electrical field components detected in the two channels. quired, which is a time consuming procedure when a com- In order to detect the phase difference between the fields in plete mapping of a transmission line containing several po- the two channels, a more sophisticated technique is required. larizers is needed. The authors in Ref. 11 used a rotating For the description and operation of this device, which is birefringent plate in front of a detector in order to character- sketched in Fig. 3, a right-handed coordinate system is con- ize an elliptically polarized wave. This technique provides all sidered, in which the wave propagates in the positive z di- three parameters of the elliptically polarized wave. The au- rection. The electrical field of the wave is perpendicular to thors in Ref. 12 introduced a method for characterization of the axis of propagation and has components in the x and y an elliptically polarized wave, in which the detected x and y directions which are referred to as Ex and Ey, respectively. components of the electrical field are added and subtracted in The axis of the detector is aligned parallel to the z axis. The a “Magic T.” Sum and difference signals are recorded. In a detector has two channels, which can detect the electrical field in two orthogonal orientations in the x-y plane simulta- neously. In order to obtain the three characteristic parameters of the elliptically polarized wave, the amplitudes of the signal in each channel and the phase between the two measured signals need to be known. The measured signal in each chan-

FIG. 4. Schematic of the transmission line in the gyrotron box at the TEXTOR-tokamak experiment. The Gunn diode is used for the measure- FIG. 2. Projection of the electrical field vector in the x-y plane. The elec- ment instead of the gyrotron as the gyrotron is too powerful and would trical field vector rotates in the mathematically negative direction ͑from the destroy the detector. The mirror M2 does not belong to the gyrotron box. It positive x axis toward the negative y axis͒ resulting in a right-hand ellipti- was only used for convenience in the measurement. The change in rotation cally polarized wave in a right handed coordinate system ͑z axis pointing of the elliptically polarized wave leaving the gyrotron box due to reflection toward the observer͒. on M2 was taken into account.

Downloaded 13 Aug 2009 to 192.38.67.112. Redistribution subject to AIP license or copyright; see http://rsi.aip.org/rsi/copyright.jsp 065103-3 Microwaves detector Rev. Sci. Instrum. 79, 065103 ͑2008͒

FIG. 5. Measured and calculated characteristics of the wave of the TEXTOR gyrotron vs the two polarizer settings at the exit of the gyrotron box. The resolution is 15°.

nel is mixed with a frequency close to 110 GHz. The goal of tokamak experiment for various polarizer settings has been this mixing is to obtain a first intermediate frequency ͑IF1͒, mapped. Figure 4 shows the quasioptical transmission in the which can be handled electrically. In order to conserve the gyrotron box before the microwaves are transmitted toward phase information between the two channels, the mixers in the plasma. The complete transmission line of the electron both channels must be fed with the same local oscillator. cyclotron resonance heating at the TEXTOR-tokamak ex- Since IF1 is given by the available local oscillator, it still can periment is detailed in Refs. 15 and 16. Horizontal linearly be too high ͑several gigahertz͒ to be detected by an oscillo- polarized light at a frequency of 110 GHz is emitted from the scope but it is sufficiently low to be processed electrically. In gyrotron. It is reflected at the mirror M1 to the polarizer UP1 this case, a second mixing stage is employed, where a tun- and from UP1 to the polarizer UP2. After the polarizer UP2, able frequency generator is used as local oscillator. Again, in the beam leaves the gyrotron box and is guided through a order to conserve the phase information, both mixers must be transmission line into the tokamak. The polarizers UP1 and fed with the same local oscillator. This means that the second UP2 are identical. Depending on the settings of UP1 and intermediate frequency ͑IF2͒ can be chosen. A typical value UP2, all possible characteristics of elliptically polarized light for IF2 is 200 MHz. A signal of this frequency can be ana- can be obtained. The gyrotron cannot be used as microwave lyzed by a fast oscilloscope. From the amplitudes of both source for the characterization of the polarizer plates, as the signals and the phase in between, the three characteristic high intensity would destroy the detector. For the measure- parameters can be calculated. ments, a Gunn diode with the same frequency as the gyrotron was placed in front of polarizer UP1 with the polarization EXPERIMENTAL SETUP orientation parallel to the polarization orientation of the Using this measuring technique, the elliptically polarized gyrotron. wave emitted from the gyrotron box at the TEXTOR- For the mapping of the polarizer settings versus the char-

Downloaded 13 Aug 2009 to 192.38.67.112. Redistribution subject to AIP license or copyright; see http://rsi.aip.org/rsi/copyright.jsp 065103-4 Leipold, Nielsen, and Michelsen Rev. Sci. Instrum. 79, 065103 ͑2008͒ acteristics of the polarization of the beam, our detector was The manufacturer of the gyrotron provided a specifica- placed at the exit of the gyrotron box ͑Fig. 4͒. Prior to the tion of each polarizer in the gyrotron box, in which the phase measurements, a calibration of the detection device needs to shift between light reflected on top of the grooves and light be done. The calibration consists of an amplitude calibration reflected at the bottom of the grooves was specified versus for each channel and a phase calibration between the two the polarizer rotation angle. Based on this characteristic, the channels. characteristic of the light expected at the exit of the gyrotron If both polarizers are tuned to their zero position, the box was calculated. The calculations for the three character- grooves are parallel to the orientation of the electrical field. istic parameters are shown in Fig. 5, right column. The cal- This means that the wave, seen at the detection device, is culations were done with the same resolution ͑15° steps͒ as also linearly polarized. The orientation of the device is cho- the measurements for better comparison. sen so that the major axes of the device do not coincide with the direction of the linearly polarized electrical field. Each CONCLUSIONS channel sees a component of the linearly polarized electrical The excellent agreement between measurement and cal- field, which must have the same phase. The detected phase culation of the microwave beam profile within the resolution difference between both channels is due to the different of 15° demonstrates the reliability of the operation of the transmission lengths in both channels. The detected phase measurement technique. This device allows to map transmis- difference is used for phase calibration. sion lines where polarizer plates with unknown characteris- For the intensity calibration, the polarizer plates were tics are included. It also allows to map the beam character- varied until one channel in the device did not show a signal. istics if transmission lines are used for various frequencies. Therefore, all intensity goes to the other channel. The mea- The device was made for frequencies around 110 GHz, but sured signal served as calibration. The same was done for the the method can, in principle, be used for any frequency in the other channel. millimeter wave range.

ACKNOWLEDGMENTS RESULTS The authors would like to thank Dr. Paul Woskov For the mapping, both polarizers were rotated from 0° to ͑PSFC, MIT͒ for discussion and the FOM group at the 180° in 15° increments, for which measurements were taken. TEXTOR-tokamak experiment for supporting these experi- The three characteristic parameters were obtained from the ments at the gyrotron box ͑110 GHz͒. amplitudes of the signal of each channel and the phase shift between the signals of both channels. The results are plotted 1 J. Wesson, Tokamaks, 2nd ed. ͑Oxford, New York, 1997͒. in Fig. 5, left column. The measurements were performed 2 M. Thumm, Plasma Phys. Controlled Fusion 45, A143 ͑2003͒. 3 ͑ ͒ with a Gunn diode and a horn antenna. The Gunn diode had M. Thumm and W. Kasparek, IEEE Trans. Plasma Sci. 30,755 2002 . 4 D. Wagner and F. Leuterer, Int. J. Infrared Millim. Waves 26,163͑2005͒. a power on the order of 20 mW. The beam of the Gunn diode 5 Y. L. Kok and N. C. Gallagher, J. Opt. Soc. Am. A 5,65͑1988͒. was expanded, so only a fraction of the power ͑less than 6 H. Bindslev, J. Atmos. Terr. Phys. 58, 983 ͑1996͒. 1mW͒ was received by the pickup waveguides. The oscillo- 7 H. Bindslev, S. K. Nielsen, L. Porte, J. A. Hoekzema, S. B. Korsholm, F. scope recorded a signal on the order of 10 mV. The accuracy Meo, P. K. Michelsen, S. Michelsen, J. W. Oosterbeek, E. L. Tsakadze, E. Westerhof, P. Woskov, and the TEXTOR team, Phys. Rev. Lett. 97, of the detector is basically given by the accuracy of the mea- 205005 ͑2006͒. surement of the voltage and the phase between both signals. 8 M. Born and E. Wolf, Principles of Optics ͑Pergamon, Oxford, 1965͒, pp. 25–30. However, two special cases shall be considered in more de- 9 tail. First, when the detected light is almost linearly polar- R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light ͑North-Holland, Amsterdam, 1977͒. ized, the phase shift between the signal is 0 ͑180°͒. Fluctua- 10 M. V. Klein and T. E. Furtak, Optik ͑Springer, Berlin, 1988͒. tions of the phase measurement around 0 ͑180°͒ results in a 11 H. Ikezi, C. P. Moeller, J. L. Doane, M. DiMartino, J. Lohr, D. Ponce, and change from left-hand polarized light to right-hand polarized R. W. Callis, Rev. Sci. Instrum. 70, 1994 ͑1999͒. 12 T. Notake, H. Idei, S. Kubo, T. Shimozuma, Y. Yoshimura, S. Kobayashi, light. In practice, this is not relevant, since the light pattern Y. Mizuno, S. Ito, Y. Takita, K. Ohkubo, W. Kasparek, T. Watari, and R. projected into the x-y plane is an extremely elongated ellipse Kumazawa, Rev. Sci. Instrum. 76, 023504 ͑2005͒. ͑␧ close to 0͒. Second, when the detected light is circularly 13 H. J. Hartfuss, T. Geist, and M. Hirsch, Plasma Phys. Controlled Fusion polarized ͑a circle in the x-y-plane projection͒, the angle of 39, 1693 ͑1997͒. 14 F. Leipold, R. H. Stark, A. El-Habachi, and K. H. Schoenbach, J. Phys. D: ellipticity is not deﬁned, as minor and major axes are iden- Appl. Phys. 33, 2268 ͑2000͒. tical. Slight ﬂuctuations in the measurement cause a change 15 N. J. Dobbe, A. B. Sterk, R. P. J. J. M. Kruisbergen, O. G. Kruyt, M. E. from the circle to an ellipse whereas the direction of the Bestbreurtje, P. R. Prins, J. A. Hoekzema, A. F. van der Grift, and B. S. Q. ͑ ͒ major axis and consequently, the angle of ellipticity cannot Elzendoorn, Fusion Eng. Des. 56, 599 2001 . 16 E. Westerhof, J. A. Hoekzema, G. M. D. Hogeweij, R. J. E. Jaspers, F. C. be predicted. In order to obtain an estimate of the accuracy of Schuller, C. J. Barth, W. A. Bongers, A. J. H. Donne, P. Dumortier, A. F. the measurements, the values between polarizer settings of van der Grift, J. C. van Gorkom, D. Kalupin, H. R. Koslowski, A. Kramer- 0° and 180° have been compared and the same results were Flecken, O. G. Kruijt, N. J. L. Cardozo, P. Mantica, H. J. van der Meiden, expected. For a wave with an ellipticity ␧ greater than 0.1, A. Merkulov, A. Messiaen, J. W. Oosterbeek, T. Oyevaar, A. J. Poelman, R. W. Polman, P. R. Prins, J. Scholten, A. B. Sterk, C. J. Tito, V. S. the measurement was reproduced within an error of 3%. The Udintsev, B. Unterberg, M. Vervier, and G. van Wassenhove, Nucl. Fusion angle of ellipticity was accurate within 4°. 43, 1371 ͑2003͒.

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